Goals from Nunez and Salah sealed a 2-0 win for the Anfield side, which moved Liverpool five points clear at the top of the Premier League ahead of the international break, but Alexander-Arnold's injury overshadowed the victory.
The England defender lasted just 25 minutes in the first half. Despite receiving treatment for three minutes, Arnold left the pitch clutching his right hamstring (injured right leg) before being replaced by Conor Bradley.
Liverpool manager Arne Slot has ruled Alexander-Arnold out of England's Nations League games against Greece and the Republic of Ireland next week, saying the 26-year-old's reaction to the injury "is not a good sign".
"It's hard to say how serious Arnold's injury is, but it looked serious when he came off in the first half. He asked to come off, not because he was tired, but because he felt something was wrong," he said.
Liverpool have won 15 of their 17 games under Slot since he was appointed as Jurgen Klopp's successor this summer, sitting top of the Premier League and Champions League.
But with home games against Real Madrid and Man City within five days of the international break, Slot warned Liverpool must stay focused in the challenging road ahead.
He said: "If I look at the upcoming matches, Liverpool will have a lot of difficulties. Overall, it will be a challenging season for us. The gap between the teams is very small, we create a gap with the opponents but not a big one. Many challenges await us.
It's a long season, we have to keep going because Man City, Arsenal, Chelsea can win as much as we can. It's never going to be easy but we'll give it our all."
